1. Identifiability of some space dependent coefficients in a wave equation of nonlinear acoustics.
- Author
-
Kaltenbacher, Barbara
- Subjects
NONLINEAR acoustics ,NONLINEAR wave equations ,SOUND pressure ,SPEED of sound ,PARAMETER identification ,INVERSE functions - Abstract
In this paper we prove uniqueness for some parameter identification problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity parameter, sound speed, and attenuation parameter, and the observation available is a single time trace of the acoustic pressure on the boundary. This is a setting relevant to several ultrasound based tomography methods. Our approach relies on the Inverse Function Theorem, which requires to prove that the forward operator is a differentiable isomorphism in appropriately chosen topologies and with an appropriate choice of the excitation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF